Localization of quantum walks on finite graphs
Hu Yang-Yi, Chen Ping-Xing†,
       

Comparison of the probability distribution of the IDTQW evolved by assigning quantum coin operation in a U(2) group with random parameters in a different range to each step of the walk to that of the Hadamard walk. Curve a: the walk using parameters assigned from ξ, ς ∈ {0, π/2} and θ ∈ {π/4, π/2}; curve b: the walk using parameters assigned from ξ, ς ∈ {0, π/2} and θ ∈ {0, π/4}; curve c: the walk using parameters assigned from ξ, θ, ς ∈ {0, π/2} for Tξ,θ,ς; curve d Hadamard walk, which is the standard form of the IDTQW with identical coin (θ = π/4); curve e the walk using T0,π/8,0. Localization is seen in the case of curve (a). The distribution is after 200 steps of the walk on a particle with initial state at origin We could see in case a the quantum walks suffer from localization.